The present invention relates to the compensation of gravity deflections in navigation systems and, more particularly, relates to an inertial navigation system having a memory that stores gravity compensation values for the compensation of gravity deflections.
An inertial navigation system is a self-contained system that uses inertial sensors and a system processor to determine velocity and position of a vehicle. The inertial sensors typically include a set of accelerometers on the vehicle that measure linear acceleration along three axes of the vehicle. The system processor integrates the acceleration data according to classical Newtonian mechanics in order to estimate the velocity and position of the vehicle.
These estimates of velocity and position have an inaccuracy resulting from an inability of the accelerometers to distinguish between vehicle acceleration and gravitational acceleration. That is, instead of measuring only vehicle acceleration, the accelerometers measure the vector sum of vehicle acceleration and gravitational acceleration. This sum is known as specific force acceleration. As a result, an accurate determination of the actual vehicle acceleration requires the navigation system to compensate for the effect of gravity on the accelerometers. This compensation involves adding (or subtracting) a gravitation term to (or from) the outputs of the accelerometers and to calculate velocity and position based upon the adjusted accelerations.
Unfortunately, gravity is not uniform around Earth. Therefore, the gravitation compensation terms used to adjust the outputs of accelerometers are typically generated by modeling Earth (or other celestial body) as an ellipsoid with a purely vertical gravitational field. Vertical means perpendicular to a plane that is tangent to the ellipsoid at the point of interest. Thus, if Earth were a sphere, its purely vertical field would extend radially from its center and, therefore, a single gravity compensation term would be used to model Earth and to compensate for the effects of gravity on the outputs of the accelerometers.
However, Earth""s shape is more irregular than the model, and therefore, Earth""s gravitational field is much more irregular than the model suggests. That is, Earth""s gravitational field not only varies in magnitude according to distance from Earth but also in direction according to local geographic features such as mountains, ocean trenches, etc. In other words, Earth""s gravitational field (and indeed that of any imperfectly shaped celestial body) deviates from a strictly vertical direction due to these geographic anomalies. These deviations are known as gravity deflections.
Gravity deflections, typically measured as North and East angles of deflection from the vertical, can have magnitudes on the order of ten micro-radians (xcexc rad) and higher. For example, the 34,000-feet-deep Kuril trench, stretching along the North Pacific airway between the U.S. and the Far East, generates gravity deflections exceeding 300 micro-radians. Deflections of this magnitude drive the velocity and position estimates of conventional inertial navigation systems outside acceptable performance bounds. As a consequence, vehicles using these conventional inertial navigation systems are apt to weave, or oscillate, about their desired courses, wasting time and fuel in the process, and adversely affecting the accuracy of inertial navigation systems.
To meet these concerns, high-precision navigation systems have implemented various compensation schemes. These schemes have included using statistical estimators to estimate the deflections, gravimeters to measure actual gravitation, and two-dimensional polynomial models to compute the deflections. Although these schemes improve accuracy, they are also quite costly in terms of computational overhead and/or hardware complexity, especially for the comparatively modest demands of commercial systems.
U.S. Pat. No. 5,774,832 discloses a navigation system incorporating a memory that stores gravity compensation data. The processor then accesses the stored gravity compensation data, based on position of the vehicle, in order to compensate for the gravity sensed by on-board inertial sensors. To conserve memory, the gravity compensation data is compressed. However, even using the data compression techniques disclosed in the ""832 patent, the amount of stored data still exceeds the capacity of many practical memories.
Accordingly, the present invention is directed to a compression technique for the compression of gravitational deflection data that solves one or more of these or other problems.
According to one aspect of the present invention, a vehicle navigation method comprises the following: generating an inertial sensor signal relating to a navigational parameter of a vehicle; accessing discrete wavelet coefficients from a memory based on a position of the vehicle; performing an inverse discrete wavelet transform on the discrete wavelet coefficients to produce compensation data; and, compensating the inertial sensor signal based on the compensation data.
According to another aspect of the present invention, a method comprises the following: performing a discrete wavelet transform on raw gravitational deflection data to produce coefficients; performing a lossless compression on the coefficients to produce compressed coefficients; and, storing the compressed coefficients in a memory of a vehicle navigation system.
According to still another aspect of the present invention, a method uses compressed wavelet transform coefficients in order to correct outputs of inertial sensors for gravitational deflections. The compressed wavelet transform coefficients comprise gravitational deflection data that is first converted to discrete wavelet coefficients by a discrete wavelet transform and that is then compressed to form the compressed wavelet transform coefficients. The method comprises the following: generating an inertial sensor signal relating to a navigational state of a vehicle; accessing the compressed discrete wavelet coefficients from a memory based on a position of the vehicle; decompressing the accessed coefficients; performing an inverse discrete wavelet transform on the decompressed coefficients to produce gravitational compensation data; and, compensating the inertial sensor signal based on the gravitational compensation data.